This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α-stable Lvy noise. We prove the main result for the stochastic equilibrium states for the original system and the reduced system based on the random slow manifold. Then, it is verified that the slow reduced system bears the stochastic bifurcation phenomenon inherited from the original system. Furthermore, we investigate the number and stability type of stochastic equilibrium states for dynamical systems through numerical simulations, and it is illustrated that the slow reduced system captures the stochastic bifurcation of the original system.

中文翻译：

---

具有α稳定Lvy噪声的二阶动力系统的随机分叉

这项工作集中在由非高斯α稳定Lvy噪声驱动的慢速动力学系统的随机分叉上。我们证明了基于随机慢流形的原始系统和简化系统的随机平衡状态的主要结果。然后，验证了慢速缩减系统具有从原始系统继承的随机分叉现象。此外，我们通过数值模拟研究了动力系统的随机平衡态的数量和稳定性类型，并证明了慢速缩减系统捕获了原始系统的随机分叉。